This section focuses on \(\delta \) -contracted compressors under assum1, where we propose COLD and explicitly derive its linear convergence rate. The novelty of COLD lies in compressing an innovation vector, which is the discrepancy between the true value of a decision vector and its estimate. Note that innovation is an important concept in the Kalman filtering theory where it represents the discrepancy between the measurements vector and their optimal predictor [1]}. Since the innovation is expected to asymptotically decrease to 0, the compression error vanishes eventually, which is key to the development of COLD. We elaborate this idea by firstly revisiting the distributed consensus problem and provide a strictly improved rate over CHOCO-GOSSIP [2]}.
